tau3scen1new {chi2x3way} R Documentation

## Marcotorchino's index for three-way contingency tables under Scenario 1. Revised formulation.

### Description

It provides the partition of the Marcotorchino's index and of the \$C_M\$-statistic, revised formula, under the Scenario 1 when probabilities are set homogeneous.

### Usage

```tau3scen1new(X, pi=rep(1/dim(X)[[1]],dim(X)[[1]]), pj=rep(1/dim(X)[[2]],dim(X)[[2]]),
pk=rep(1/dim(X)[[3]],dim(X)[[3]]), digits = 3)
```

### Arguments

 `X` The three-way contingency table. `pi` The input parameter for specifying the theoretical probabilities of rows categories. When `scen = 1`, they can be prescribed by the analyst. By default, they are set equal among the categories, homogeneous margins (uniform probabilities), that is `pi = rep(1/dim(X)[[1]],dim(X)[[1]])`. `pj` The input parameter for specifying the theoretical probabilities of columns categories. When `scen = 1`, they can be prescribed by the analyst. By default, they are set equal among the categories, homogeneous margins (uniform probabilities), that is `pj = rep(1/dim(X)[[2]],dim(X)[[2]])`. `pk` The input parameter for specifying the theoretical probabilities of tube categories. When `scen = 1`, they can be prescribed by the analyst. By default, they are set equal among the categories, homogeneous margins (uniform probabilities), that is `pk = rep(1/dim(X)[[3]],dim(X)[[3]])`. `digits` The minimum number of decimal places, `digits`, used for displaying the numerical summaries of the analysis. By default, `digits = 3`.

### Value

Description of of the output returned

 `z` The Marcotorchino's index partition under Scenario 1, we get seven terms partitioning the Marcotorchino's index and the revised \$C_M\$-statistic, three main terms, two bivariate terms and a trivariate term. The output is in a matrix, the six rows of this matrix indicate the tau index numerator, the tau index, the percentage of explained inertia, the revised \$C_M\$-statistic, the degree of freedom, the p-value, respectively.

### Note

This function belongs to the class `chi3class`.

### Author(s)

Lombardo R, Takane Y and Beh EJ

### References

Beh EJ and Lombardo R (2014) Correspondence Analysis: Theory, Practice and New Strategies. John Wiley & Sons. Lancaster H O (1951) Complex contingency tables treated by the partition of the chi-square. Journal of Royal Statistical Society, Series B, 13, 242-249.
Loisel S and Takane Y (2015) Partitions of Pearson's chi-square statistic for frequency tables: A comprehensive account. Computational Statistics, 31, 1429-1452.
Lombardo R Carlier A D'Ambra L (1996) Nonsymmetric correspondence analysis for three-way contingency tables. Methodologica, 4, 59-80.
Marcotorchino F (1985) Utilisation des comparaisons par paires en statistique des contingencies: Partie III. Etude du Centre Scientifique, IBM, France. No F 081

### Examples

```data(olive)
tau3scen1new(olive)
```

[Package chi2x3way version 1.1 Index]